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Take Your Base July 7, 2011

Posted by tomflesher in Baseball, Economics.
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As usual, Kevin Youkilis is getting hit at an alarming rate this year. A quick check of his stats from Baseball Reference shows that from 2004 to 2010, he got hit at about a 2% clip and was intentionally walked about .5% of the time. This year, he’s been hit nine times in 340 plate appearances, for about 2.6% of plate appearances ending in the phrase “Take your base.” He’s only been intentionally walked once, which isn’t out of line from his three IBBs last year. In contrast, he was “only” hit ten times last year, so he’s one away from eclipsing that mark and six away from tying his record 15 times hit (in 2007). Interestingly, Kevin has never been hit in the postseason.

It would be oversimplistic to say that guys who get hit a lot get hit because they’re jerks. There’s a plausible argument that Youkilis’ unorthodox batting stance is responsible for his high rate, and some guys just get hit more often. Crashburn Alley makes the point that getting hit is a legitimate skill, and Plunk Everyone has a truly dizzying array of information about players getting hit. My question, though, is whether it could be the case that Youkilis is hit less often in the postseason because pitchers are more careful.

In 2007, 2008, and 2009, Youkilis made a total of 123 postseason plate appearances. During that time, he was never hit, nor was he intentionally walked. His OBP was .376, compared with a .397 regular-season OBP over those years. It’s possible that he was simply slumping and not seen as a threat.

It’s also possible that Youk’s failure to get hit at a respectable 2% rate (we’d have expected about 2 1/2 plunks) was simply chance. As a quick check, assume that his regular season stats during 2007, 2008, and 2009 represent “true” information, and that the 123 plate appearances he made in the postseasons were all random draws from the same distribution. Since he was hit 43 times in 1834 plate appearances across 2007-09, his true rate would be 2.3% (closer to 2.34, but I rounded down – note that this cuts Youk a little extra slack). Then, 95% of 123-appearance distributions should have hit-by-pitch rates that fall within the window

.023 \pm 2*se

where se is the standard error, calculated as

\sqrt{\frac{p(1-p)}{n-1}} = \sqrt{\frac{.023(.977)}{122}} \approx .0135

Thus, 95 out of 100 123-appearance runs should fall within the window

(.023 - 2*.0135, .023 + 2*.0135) = (-.004, .05)

Obviously, since there can’t be a negative number of hit batsmen, zero is included in that interval. Youkilis isn’t necessarily being pitched around more effectively in the postseason – he’s just unlucky enough not to get plunked.

Hit Batsman Roundup, 2010 December 26, 2010

Posted by tomflesher in Baseball.
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There’s very little more subtle and involved than the quiet elegance of a batter getting beaned. In fact, that particular strategy was invoked 1549 times in 2010, with 419 batters getting plunked at least one.

The absolute leader this season was not Kevin Youkilis or Brett Carroll but Rickie Weeks, who led with 25 HBP in 754 plate appearances. Put another way, Weeks got hit in 3.32% of his plate appearances.  That’s almost once every 30 plate appearances, or nearly four times the MLB-wide rate of 0.83% of the time. (Incidentally, that’s total HBP divided by total plate appearances. The more skewed mean percentage is 0.58%.) What leads to such a high number of plunkings?

I would assume that a few things would go into the decision to hit a batter intentionally:

  • Pitchers are less likely to be hit by other pitchers.
  • If a hitter is likely to get on base anyway, he’s more likely to be hit – you don’t lose anything by putting him on base, and you control the damage by limiting him to one base.
  • If a batter is likely to hit for extra bases, he’s more likely to be hit.
  • If a batter is likely to steal a base, he’s less likely to be hit, but there is an offsetting effect for caught stealing.
  • American League batters are more likely to be hit because of the moral hazard effect of pitchers not having to bat.

With that in mind, I set up a regression in R using every player who had at least one plate appearance in 2010. I added binary variables for Pitcher (1 if the player’s primary position is pitcher, 0 otherwise) and Lg (1 if the player played the entire season in the American League, 0 otherwise), then regressed HBP/PA on Pitcher, Lg, BB, HR, OBP, SLG, SB, and CS. The results were somewhat surprising:

Call:
lm(formula = hbppa ~ Pitcher + Lg + BB + HR + OBP + SLG + SB + 
    CS)
 
Residuals:
       Min         1Q     Median         3Q        Max 
-0.0154027 -0.0059081 -0.0018096  0.0001845  0.1397065 
 
Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  6.847e-03  9.815e-04   6.975 5.77e-12 ***
Pitcher     -5.399e-03  9.136e-04  -5.909 4.81e-09 ***
Lg          -1.614e-03  7.054e-04  -2.289   0.0223 *  
BB          -1.412e-05  3.257e-05  -0.434   0.6647    
HR           1.122e-04  7.956e-05   1.411   0.1587    
OBP          8.570e-03  3.477e-03   2.465   0.0139 *  
SLG         -3.451e-03  2.468e-03  -1.398   0.1624    
SB          -6.749e-05  8.693e-05  -0.776   0.4377    
CS           1.770e-04  2.646e-04   0.669   0.5036    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
 
Residual standard error: 0.01042 on 935 degrees of freedom
Multiple R-squared: 0.08839,    Adjusted R-squared: 0.08059 
F-statistic: 11.33 on 8 and 935 DF,  p-value: 2.07e-15

Created by Pretty R at inside-R.org

That’s right – only Pitcher, Lg, HR, and SLG are even marginally significant (80% level). BB, SB, and CS aren’t even close. Why not?

Well, for one, the number of stolen bases and times caught stealing are relatively small no matter what. There probably isn’t enough data. For another, there simply probably isn’t as much intent to hit batters as we’d like to pretend.

Second, American Leaguers are less likely to be hit. This baffles me a little bit.

Also, keep in mind that this model shouldn’t be expected to, and cannot, explain all or even most of the variation in hit batsman. The R-squared is about .09, meaning that it explains about 9% of the variation. It ignores probably the most important factor, physics, entirely. (That is, the model doesn’t have any way to account for accidental plunkings.) As a side note, other regressions show there might be an effect for plate appearances, meaning you’re more likely to get hit by chance alone if you take enough pitches.

Finally, there are some guys who manage to do the opposite of Weeks’ feat. Houston outfielder Hunter Pence went 156 games and 658 plate appearances without getting plunked at all. Honorable mentions go to Raul Ibanez, Scott Podsednik, Victor Martinez, and Omar Infante, all of whom went over 500 plate appearances without a beaning. Now THAT’S plate discipline.

How often should Youk take his base? June 30, 2010

Posted by tomflesher in Baseball, Economics.
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Kevin Youkilis is sometimes called “The Greek God of Walks.” I prefer to think of him as “The Greek God of Take Your Base,” since he seems to get hit by pitches at an alarming rate. In fact, this year, he’s been hit 7 times in 313 plate appearances. (Rickie Weeks, however, is leading the pack with 13 in 362 plate appearances. We’ll look at him, too.) There are three explanations for this:

  1. There’s something about Youk’s batting or his hitting stance that causes him to be hit. This is my preferred explanation. Youkilis has an unusual batting grip that thrusts his lead elbow over the plate, and as he swings, he lunges forward, which exposes him to being plunked more often.
  2. Youkilis is such a hitting machine that the gets hit often in order to keep him from swinging for the fences. This doesn’t hold water, to me. A pitcher could just as easily put him on base safely with an intentional walk, so unless there’s some other incentive to hit him, there’s no reason to risk ejection by throwing at Youkilis. This leads directly to…
  3. Youk is a jerk. This is pretty self-explanatory, and is probably a factor.

First of all, we need to figure out whether it’s likely that Kevin is being hit by chance. To figure that out, we need to make some assumptions about hit batsmen and evaluate them using the binomial distribution. I’m also excited to point out that Youk has been overtaken as the Greek God of Take Your Base by someone new: Brett Carroll. (more…)

Does the DH Rule Cause Batters to be Hit? June 2, 2010

Posted by tomflesher in Baseball, Economics.
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In an earlier post, I crunched some numbers on the Designated Hitter rule and came to the conclusion that the DH adds about .3 extra trips to first base per game after accounting for trend. I’m going to play around with another stat that a lot of people seem to think should be affected indirectly by the DH rule.

The Conventional Wisdom™ is that the DH should increase hit batsman. The argument is that pitchers don’t bear the costs of hitting a batter with a pitch because they don’t bat, so they’ll be less careful to avoid hitting a batter or more likely to plunk a batter out of malice. Do the numbers bear that out?

(more…)